Geophysical Inversion

Syllabus: 

  • Basic concepts of forward and inverse problems 
  • Ill-posedness of inverse problems, 
  • condition number, non-uniqueness and stability of solutions; 
  • L1, L2 and Lp norms
  • overdetermined, underdetermined and mixed determined inverse problems,
  • quasi- linear and non-linear methods including Tikhonov’s regularization method, 
  • Singular Value Decomposition, 
  • Backus-Gilbert method, 
  • simulated annealing, 
  • genetic algorithms, 
  • swarm intelligence, 
  • machine learning and artificial neural networks. 
  • Statistics of misfit and likelihood, 
  • Bayesian construction of posterior probabilities,
  • sparsity promoting L1 optimization. 
  • Ambiguity and uncertainty in geophysical interpretation.
  • Optimization
  • Null-Space
GATE questions